A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators
The purpose of this paper is to introduce a new iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of variational inequality problems, the zero point of maximal monotone operators, and the set of two countable familie...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/692829 |
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| Summary: | The purpose of this paper is to introduce a new iterative scheme for finding a common
element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of
variational inequality problems, the zero point of maximal monotone operators, and the set of two
countable families of quasi-ϕ-nonexpansive mappings in Banach spaces. Moreover, the strong convergence
theorems of this method are established under the suitable conditions of the parameter imposed
on the algorithm. Finally, we apply our results to finding a zero point of inverse-strongly monotone
operators and complementarity problems. Our results presented in this paper improve and extend
the recently results by many others. |
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| ISSN: | 1110-757X 1687-0042 |